1. Field of the Invention
The present invention relates to a 2N-point and N-point fast Fourier transform (FFT)/inverse fast Fourier transform (IFFT) dual mode processor, and more particularly, to a 2N-point and N-point FFT/IFFT dual mode processor for allowing a 2N-point FFT processor and a N-point FFT processor to operate in a dual mode in achieving an IFFT/FFT processor used in a orthogonal frequency division multiplexing (OFDM) system.
2. Description of the Related Art
As known in the art, OFDM means a method for dividing data having a high-speed transmission rate into a plurality of data lines having a low-speed transmission rate and simultaneously transmitting the plurality of data lines using a plurality of sub-carrier waves. A process for making such sub-carrier waves and conveying the data on the sub-carrier waves is an IFFT/FFT operation. The transmission terminal of OFDM requires an IFET operation so as to convey data on a plurality of sub-carrier waves, and the reception terminal of OFDM requires an FET operation so as to obtain data from a plurality of sub-carrier waves.
FIG. 1 is a block diagram illustrating processes performed by an IFFT processor of the transmission terminal and by an FFT processor of the reception terminal. Referring to FIG. 1, an N-point IFFT processor 10 of an OFDM system conveys data on n sub-carrier waves. At this point, after a guard interval (GI) is added to an N-point IFFT-processed signal at a next block 11, an N-point IFFT-processed signal is delivered to a digital-to-analog converter (DAC) 12. After that, the spectrum of a signal from the DAC 12 has frequency spectrum waveforms 1a, 1b, and 1c as illustrated in FIG. 2A. A low pass filter (LPF) 13 is used to pass only a baseband signal component 1a from the repeated frequency components.
FIG. 2 is a view illustrating the spectrum of an N-point IFFT signal after the DAC 12 of the transmission terminal illustrated in FIG. 1. At this point, the frequency spectrums 1a, 1b, and 1c of a signal are repeated by a period F(b). To convey a signal on a carrier wave frequency, only a baseband signal component 1a should be obtained and the other signal components 1b and 1c should be removed. For that purpose, the LPF 13 is required as described above.
The above obtained baseband signal 1a is wirelessly transmitted through a local oscillator 14 and an antenna 15. The reception terminals 16, 17, and 18 recover data using reverse processes with respect to the processes performed at the transmission terminals 11 to 15. Referring to FIG. 1, the OFDM system requires the N-point IFFT processor 10 of the transmission terminal and the N-point FFT processor 18 of the reception terminal. At this point, the IFFT processor can be replaced by the FFT processor. That is, when inputs of the real part and the imaginary part in the FFT processor are exchanged and the real part and the imaginary part of an output are exchanged, the IFFT operation can be possible. The proof thereof can be provided when A(k) and B(k) of Equation 1 is compared with a(n) and b(n) of Equation 2 in the following Equations 1 and 2.
                                          FFT            ⁢                          :                        ⁢                                                  ⁢                          X              ⁡                              (                k                )                                              =                                    ∑                              n                =                0                                            N                -                1                                      ⁢                                          x                ⁡                                  (                  n                  )                                            ⁢                              ⅇ                                                      -                    j                                    ⁢                                                            2                      ⁢                      π                                        N                                    ⁢                  kn                                                                    ⁢                                  ⁢                                            X              ⁡                              (                k                )                                      =                                          A                ⁡                                  (                  k                  )                                            +                              j                ⁢                                                                  ⁢                                  B                  ⁡                                      (                    k                    )                                                                                ,                                          ⁢                                    x              ⁡                              (                n                )                                      =                                          a                ⁡                                  (                  n                  )                                            +                              j                ⁢                                                                  ⁢                                  b                  ⁡                                      (                    n                    )                                                                                      ⁢                                  ⁢                  so          ⁢                                          ⁢          that                ⁢                                  ⁢                                                                                                  A                    ⁡                                          (                      k                      )                                                        +                                      j                    ⁢                                                                                  ⁢                                          B                      ⁡                                              (                        k                        )                                                                                            =                                                      ∑                                          n                      =                      0                                                              N                      -                      1                                                        ⁢                                                            {                                                                        a                          ⁡                                                      (                            n                            )                                                                          +                                                  j                          ⁢                                                                                                          ⁢                                                      b                            ⁡                                                          (                              n                              )                                                                                                                          }                                        ⁢                                          {                                                                        cos                          ⁡                                                      (                                                          j                              ⁢                                                                                                2                                  ⁢                                  π                                                                N                                                            ⁢                              kn                                                        )                                                                          -                                                  j                          ⁢                                                                                                          ⁢                                                      sin                            ⁡                                                          (                                                              j                                ⁢                                                                                                      2                                    ⁢                                    π                                                                    N                                                                ⁢                                kn                                                            )                                                                                                                          }                                                                                                                                              =                                                      ∑                                          n                      =                      0                                                              N                      -                      1                                                        ⁢                                      [                                                                  {                                                                                                            a                              ⁡                                                              (                                n                                )                                                                                      ⁢                            cos                            ⁢                                                                                                                  ⁢                                                          θ                              kn                                                                                +                                                                                    b                              ⁡                                                              (                                n                                )                                                                                      ⁢                            sin                            ⁢                                                                                                                  ⁢                                                          θ                              kn                                                                                                      }                                            +                                              j                        ⁢                                                  {                                                                                                                    -                                                                  a                                  ⁡                                                                      (                                    n                                    )                                                                                                                              ⁢                              sin                              ⁢                                                                                                                          ⁢                                                              θ                                kn                                                                                      +                                                                                          b                                ⁡                                                                  (                                  n                                  )                                                                                            ⁢                              cos                              ⁢                                                                                                                          ⁢                                                              θ                                kn                                                                                                              }                                                                                      ]                                                                                      ⁢                                  ⁢                              A            ⁢                          (              k              )                                =                                    ∑                              n                =                0                                            N                -                1                                      ⁢                          {                                                                    a                    ⁡                                          (                      n                      )                                                        ⁢                  cos                  ⁢                                                                          ⁢                                      θ                    kn                                                  +                                                      b                    ⁡                                          (                      n                      )                                                        ⁢                  sin                  ⁢                                                                          ⁢                                      θ                    kn                                                              }                                      ⁢                                  ⁢                              B            ⁢                          (              k              )                                =                                    ∑                              n                =                0                                            N                -                1                                      ⁢                          {                                                                    -                                          a                      ⁡                                              (                        n                        )                                                                              ⁢                  sin                  ⁢                                                                          ⁢                                      θ                    kn                                                  +                                                      b                    ⁡                                          (                      n                      )                                                        ⁢                  cos                  ⁢                                                                          ⁢                                      θ                    kn                                                              }                                                          Equation        ⁢                                  ⁢        1            
                                          IFFT            ⁢                          :                        ⁢                                                  ⁢                          X              ⁡                              (                n                )                                              =                                    ∑                              k                =                0                                            N                -                1                                      ⁢                                          X                ⁡                                  (                  k                  )                                            ⁢                              ⅇ                                  j                  ⁢                                                            2                      ⁢                      π                                        N                                    ⁢                  kn                                                                    ⁢                                  ⁢                                                                                                  a                    ⁡                                          (                      n                      )                                                        +                                      j                    ⁢                                                                                  ⁢                                          b                      ⁡                                              (                        n                        )                                                                                            =                                                      1                    N                                    ⁢                                                            ∑                                              k                        =                        0                                                                    N                        -                        1                                                              ⁢                                                                  {                                                                              A                            ⁡                                                          (                              k                              )                                                                                +                                                      j                            ⁢                                                                                                                  ⁢                                                          B                              ⁡                                                              (                                k                                )                                                                                                                                    }                                            ⁢                                              {                                                                              cos                            ⁡                                                          (                                                              j                                ⁢                                                                                                      2                                    ⁢                                    π                                                                    N                                                                ⁢                                kn                                                            )                                                                                +                                                      j                            ⁢                                                                                                                  ⁢                                                          sin                              ⁡                                                              (                                                                  j                                  ⁢                                                                                                            2                                      ⁢                                      π                                                                        N                                                                    ⁢                                  kn                                                                )                                                                                                                                    }                                                                                                                                                                                      =                                                            1                      N                                        ⁢                                                                  ∑                                                  k                          =                          0                                                                          N                          -                          1                                                                    ⁢                                              [                                                                              {                                                                                                                            A                                  ⁡                                                                      (                                    k                                    )                                                                                                  ⁢                                cos                                ⁢                                                                                                                                  ⁢                                                                  θ                                  kn                                                                                            -                                                                                                B                                  ⁡                                                                      (                                    k                                    )                                                                                                  ⁢                                sin                                ⁢                                                                                                                                  ⁢                                                                  θ                                  kn                                                                                                                      }                                                    +                                                      j                            ⁢                                                          {                                                                                                                                    A                                    ⁡                                                                          (                                      k                                      )                                                                                                        ⁢                                  sin                                  ⁢                                                                                                                                          ⁢                                                                      θ                                    kn                                                                                                  +                                                                                                      B                                    ⁡                                                                          (                                      k                                      )                                                                                                        ⁢                                  cos                                  ⁢                                                                                                                                          ⁢                                                                      θ                                    kn                                                                                                                              }                                                                                                      ]                                                                                            ⁢                                                                  ⁢                                                      a                    ⁡                                          (                      n                      )                                                        =                                                            ∑                                              k                        =                        0                                                                    N                        -                        1                                                              ⁢                                          {                                                                                                    A                            ⁡                                                          (                              k                              )                                                                                ⁢                          sin                          ⁢                                                                                                          ⁢                                                      θ                            kn                                                                          +                                                                              A                            ⁡                                                          (                              k                              )                                                                                ⁢                          cos                          ⁢                                                                                                          ⁢                                                      θ                            kn                                                                                              }                                                                      ⁢                                                                  ⁢                                                      b                    ⁡                                          (                      n                      )                                                        =                                                            ∑                                              k                        =                        0                                                                    N                        -                        1                                                              ⁢                                          {                                                                                                    B                            ⁡                                                          (                              k                              )                                                                                ⁢                          cos                          ⁢                                                                                                          ⁢                                                      θ                            kn                                                                          +                                                                              A                            ⁡                                                          (                              k                              )                                                                                ⁢                          sin                          ⁢                                                                                                          ⁢                                                      θ                            kn                                                                                              }                                                                                                                              Equation        ⁢                                  ⁢        2            
As described above, the N-point FFT processor is replaced by the N-point IFFT processor in the OFDM system of FIG. 1.
Referring to FIG. 2, to convey a signal on a desired carrier wave frequency, only a baseband signal component 1a should be obtained and the other signal components 1b and 1c should be removed. For that purpose, the LPF 13 is required as described above. To pass only the baseband signal component 1a and remove the signal 1b having a main frequency F(b) in its frequency components, the LPF 13 having a very narrow transition band is required. However, when the transition band of the LPF 13 is larger than the interval of the repeated OFDM signal spectrum, noises are generated.
To solve such a problem, the transition band of the LPF 13 is made very narrow or the interval of the repeated OFDM signal spectrum is widened so that noises may not be generated.
At this point, when the interval between the intervals of the repeated frequency spectrums is too narrow, the LPF 13 is difficult to realize and filtering cannot be performed properly. To solve this problem, it is possible to widen the interval between the repeated frequency spectrums by inserting, at the IFFT processor, N-point ‘0’ into N-point data. In that case, the IFFT processor performs an operation using 2N-point and the FFT processor performs an operation using N-point. As described above, the N-point FFT processor and the 2N-point IFFT processor can be simultaneously required in one system.
However, in the case where the N-point FFT processor and the 2N-point IFFT processor can be simultaneously required in one system in the conventional art, the N-point FFT processor and the 2N-point FFT processor are separately and respectively designed to realize a system, so that a system design is difficult and the manufacturing costs increase.